[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.51,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.51,0:00:04.64,Default,,0000,0000,0000,,Divide and write the answer\Nas a mixed number.
Dialogue: 0,0:00:04.64,0:00:07.77,Default,,0000,0000,0000,,And we have 3/5 divided\Nby 1/2.
Dialogue: 0,0:00:07.77,0:00:10.22,Default,,0000,0000,0000,,Now, whenever you're dividing\Nany fractions, you just have
Dialogue: 0,0:00:10.22,0:00:14.20,Default,,0000,0000,0000,,to remember that dividing by a\Nfraction is the same thing as
Dialogue: 0,0:00:14.20,0:00:16.97,Default,,0000,0000,0000,,multiplying by its reciprocal.
Dialogue: 0,0:00:16.97,0:00:22.81,Default,,0000,0000,0000,,So this thing right here is the\Nsame thing as 3/5 times--
Dialogue: 0,0:00:22.81,0:00:25.78,Default,,0000,0000,0000,,so this is our 3/5 right here,\Nand instead of a division
Dialogue: 0,0:00:25.78,0:00:28.12,Default,,0000,0000,0000,,sign, you want a multiplication\Nsign, and
Dialogue: 0,0:00:28.12,0:00:31.88,Default,,0000,0000,0000,,instead of a 1/2, you want to\Ntake the reciprocal of 1/2,
Dialogue: 0,0:00:31.88,0:00:36.51,Default,,0000,0000,0000,,which would be 2/1--\Nso times 2/1.
Dialogue: 0,0:00:36.51,0:00:39.77,Default,,0000,0000,0000,,So dividing by 1/2 is the\Nexact same thing as
Dialogue: 0,0:00:39.77,0:00:42.36,Default,,0000,0000,0000,,multiplying by 2/1.
Dialogue: 0,0:00:42.36,0:00:45.00,Default,,0000,0000,0000,,And we just do this as a\Nstraightforward multiplication
Dialogue: 0,0:00:45.00,0:00:46.08,Default,,0000,0000,0000,,problem now.
Dialogue: 0,0:00:46.08,0:00:49.84,Default,,0000,0000,0000,,3 times 2 is 6, so our\Nnew numerator is 6.
Dialogue: 0,0:00:49.84,0:00:52.95,Default,,0000,0000,0000,,5 times 1 is 5.
Dialogue: 0,0:00:52.95,0:00:57.36,Default,,0000,0000,0000,,So 3/5 divided by 1/2 as an\Nimproper fraction is 6/5.
Dialogue: 0,0:00:57.36,0:01:01.22,Default,,0000,0000,0000,,Now, they want us to write\Nit as at mixed number.
Dialogue: 0,0:01:01.22,0:01:04.45,Default,,0000,0000,0000,,So we divide the 5 into\Nthe 6, figure out how
Dialogue: 0,0:01:04.45,0:01:05.30,Default,,0000,0000,0000,,many times it goes.
Dialogue: 0,0:01:05.30,0:01:07.53,Default,,0000,0000,0000,,That'll be the whole number\Npart of the mixed number.
Dialogue: 0,0:01:07.53,0:01:10.29,Default,,0000,0000,0000,,And then whatever's left over\Nwill be the remaining
Dialogue: 0,0:01:10.29,0:01:13.62,Default,,0000,0000,0000,,numerator over 5.
Dialogue: 0,0:01:13.62,0:01:18.16,Default,,0000,0000,0000,,So what we'll do is\Ntake 5 into 6.
Dialogue: 0,0:01:18.16,0:01:20.60,Default,,0000,0000,0000,,5 goes into 6 one time.
Dialogue: 0,0:01:20.60,0:01:22.70,Default,,0000,0000,0000,,1 times 5 is 5.
Dialogue: 0,0:01:22.70,0:01:23.36,Default,,0000,0000,0000,,Subtract.
Dialogue: 0,0:01:23.36,0:01:25.96,Default,,0000,0000,0000,,You have a remainder of 1.
Dialogue: 0,0:01:25.96,0:01:34.46,Default,,0000,0000,0000,,So 6/5 is equal to one whole,\Nor 5/5, and 1/5.
Dialogue: 0,0:01:34.46,0:01:38.91,Default,,0000,0000,0000,,
Dialogue: 0,0:01:38.91,0:01:42.61,Default,,0000,0000,0000,,This 1 comes from whatever\Nis left over.
Dialogue: 0,0:01:42.61,0:01:43.63,Default,,0000,0000,0000,,And now we're done!
Dialogue: 0,0:01:43.63,0:01:46.73,Default,,0000,0000,0000,,3/5 divided by 1/2\Nis 1 and 1/5.
Dialogue: 0,0:01:46.73,0:01:49.35,Default,,0000,0000,0000,,Now, the one thing that's not\Nobvious is why did this work?
Dialogue: 0,0:01:49.35,0:01:53.66,Default,,0000,0000,0000,,Why is dividing by 1/2 the\Nsame thing as multiplying
Dialogue: 0,0:01:53.66,0:01:54.88,Default,,0000,0000,0000,,essentially by 2.
Dialogue: 0,0:01:54.88,0:01:57.00,Default,,0000,0000,0000,,2/1 is the same thing as 2.
Dialogue: 0,0:01:57.00,0:01:59.89,Default,,0000,0000,0000,,And to do that, I'll do a little\Nside-- fairly simple--
Dialogue: 0,0:01:59.89,0:02:03.87,Default,,0000,0000,0000,,example, but hopefully, it\Ngets the point across.
Dialogue: 0,0:02:03.87,0:02:05.91,Default,,0000,0000,0000,,Let me take four objects.
Dialogue: 0,0:02:05.91,0:02:08.85,Default,,0000,0000,0000,,So we have four objects:\None, two, three, four.
Dialogue: 0,0:02:08.85,0:02:13.79,Default,,0000,0000,0000,,So I have four objects, and if\NI were to divide into groups
Dialogue: 0,0:02:13.79,0:02:17.30,Default,,0000,0000,0000,,of two, so I want to divide\Nit into groups of two.
Dialogue: 0,0:02:17.30,0:02:21.21,Default,,0000,0000,0000,,So that is one group of two and\Nthen that is another group
Dialogue: 0,0:02:21.21,0:02:23.60,Default,,0000,0000,0000,,of two, how many groups\Ndo I have?
Dialogue: 0,0:02:23.60,0:02:27.40,Default,,0000,0000,0000,,Well, 4 divided by 2, I have two\Ngroups of two, so that is
Dialogue: 0,0:02:27.40,0:02:28.90,Default,,0000,0000,0000,,equal to 2.
Dialogue: 0,0:02:28.90,0:02:31.46,Default,,0000,0000,0000,,Now, what if I took those\Nsame four objects:
Dialogue: 0,0:02:31.46,0:02:33.99,Default,,0000,0000,0000,,one, two, three, four.
Dialogue: 0,0:02:33.99,0:02:36.16,Default,,0000,0000,0000,,So I'm taking those\Nsame four objects.
Dialogue: 0,0:02:36.16,0:02:38.89,Default,,0000,0000,0000,,Instead of dividing them into\Ngroups of two, I want to
Dialogue: 0,0:02:38.89,0:02:44.61,Default,,0000,0000,0000,,divide them into groups of 1/2,\Nwhich means each group
Dialogue: 0,0:02:44.61,0:02:47.08,Default,,0000,0000,0000,,will have half of\Nan object in it.
Dialogue: 0,0:02:47.08,0:02:49.96,Default,,0000,0000,0000,,So let's say that would be\None group right there.
Dialogue: 0,0:02:49.96,0:02:51.90,Default,,0000,0000,0000,,That is a second group.
Dialogue: 0,0:02:51.90,0:02:53.14,Default,,0000,0000,0000,,That is a third group.
Dialogue: 0,0:02:53.14,0:02:56.69,Default,,0000,0000,0000,,I think you see each group has\Nhalf of a circle in it.
Dialogue: 0,0:02:56.69,0:02:58.28,Default,,0000,0000,0000,,That is the fourth.
Dialogue: 0,0:02:58.28,0:03:00.07,Default,,0000,0000,0000,,That's the fifth.
Dialogue: 0,0:03:00.07,0:03:01.39,Default,,0000,0000,0000,,That's the sixth.
Dialogue: 0,0:03:01.39,0:03:03.79,Default,,0000,0000,0000,,That's the seventh, and then\Nthat's the eighth.
Dialogue: 0,0:03:03.79,0:03:08.66,Default,,0000,0000,0000,,You have eight groups of 1/2,\Nso this is equal to 8.
Dialogue: 0,0:03:08.66,0:03:12.92,Default,,0000,0000,0000,,And notice, now each of the\Nobjects became two groups.
Dialogue: 0,0:03:12.92,0:03:14.66,Default,,0000,0000,0000,,So you could say how many\Ngroups do you have?
Dialogue: 0,0:03:14.66,0:03:16.86,Default,,0000,0000,0000,,Well, you have four objects\Nand each of
Dialogue: 0,0:03:16.86,0:03:21.29,Default,,0000,0000,0000,,them became two groups.
Dialogue: 0,0:03:21.29,0:03:22.27,Default,,0000,0000,0000,,I'm looking for a\Ndifferent color.
Dialogue: 0,0:03:22.27,0:03:24.52,Default,,0000,0000,0000,,Each of them became\Ntwo groups, and so
Dialogue: 0,0:03:24.52,0:03:26.84,Default,,0000,0000,0000,,you also have eight.
Dialogue: 0,0:03:26.84,0:03:30.71,Default,,0000,0000,0000,,So dividing by 1/2 is the same\Nthing as multiplying by 2.
Dialogue: 0,0:03:30.71,0:03:32.25,Default,,0000,0000,0000,,And you could think about it\Nwith other numbers, but
Dialogue: 0,0:03:32.25,0:03:35.02,Default,,0000,0000,0000,,hopefully, that gives you a\Nlittle bit of an intuition.
Dialogue: 0,0:03:35.02,0:03:35.33,Default,,0000,0000,0000,,